In the README it explains that the google-services.json file should be declared by using:
<platform name="android">
<resource-file src="google-services.json" target="google-services.json" />
</platform>
This caused the build to fail, as the file was not found by the related Gradle task.
The actual configuration should be
<platform name="android">
<resource-file src="google-services.json" target="app/google-services.json" />
</platform>
This was taken from the cordova-support-google-services page (https://www.npmjs.com/package/cordova-support-google-services) and made the build work with no problems.
Specifications
Tested on Windows 7, the following plugins:
cordova-support-google-services^1.3.1
cordova-plugin-firebaseui-auth^1.0.2
cordova-plugin-firestore^1.3.2